On Differentiability of Minimal Surfaces at a Boundary Point

Tunc Geveci
1971 Proceedings of the American Mathematical Society  
Let F(z) = {u(z), v(z), w(z)}, \z\ <1, represent a minimal surface spanning the curve T: { U(s), V(s), W(s)}, s being the arc length. Suppose T has a tangent at a point P. Then F(z) is differentiable at this point if U'(s), V'(s), W'(s) satisfy a Dini condition at P.
doi:10.2307/2037786 fatcat:ibnacvcuqbg4jdoqtevu5siogi